c) lim x-+0 tan 3x 1- Jx e) lim x 1-x g) lim(\n² +1-n)

Q: 2-limx-o(x. secx.cscx)

A: To find the limit of the following.                                     limx→0 (x sec x csc x)

Q: Compute x-+xX lim X-700 It Ttx Sinx 2) Lim X-70 CUSX-1 X3-1 1L-X

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: find: a) Lim x4-1 x2 b). Lim 10x-3 SinX

A: We have to find the following limit      alimx→1x4-1x2-1       blimx→010x-3sinxx

Q: 2) lim (+5)a00 (-2a+1)50

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: '5x2+3х-1) lim = 4x2+5) n-00

A: Divide the numerator and denominator by the highest power i.e. x^2 and simplify the limit.

Q: 4x3-2х с) lim x→00 V2x4+1

A:

Q: e lim Secx-1 Sinx (-esux) 3}r® २5 ९६० 5x 2 lim ーD6 Sin5x of Sin4x. e lim メーD6 よ + tan 38

A:

Q: x²+3x+2 b) lim x-1 x²-x-2

A: given limit

Q: 1 c) lim x+0 \ex-1 X.

A: the given expression is: limx→01ex-1-1x…

Q: lim (1+ tan 3x)*

A:

Q: g) 1/(2lnx) lim(1+2x)"

A: a) Here we have to find the limit of function f(x)=(1+2x)12lnx as x→∞limx→∞ f(x)=limx→∞…

Q: V5x+4-3 3) lim X-1 x-1

A:

Q: d) (x+27) -3 X lim-

A:

Q: 1. Evaluate. 3x -14 a) lim- -4 x-2 r²+x-12 b) lim x-3

A:

Q: lim as x goes to -3 of (4(2x+1)^2-100)/x+3

A:

Q: x-sin x b) lim x3

A: For the given    is calculated using expansion of sin x as shown  below

Q: 4- Prove that lim- tan 2x 5-lim 2(-3+x)²-18) x-0 X-0 2.

A:

Q: b) 49-(5+ x)² x-2 lim-

A: Use L.Hospital rule to evaluate above limit as in next step.

Q: lim x>-3- x² +2xr-3 a. X- 7X b. lim x>-3+ x2 +2x-3 lim x>-3 x² +2x-3 C. X- ,X

A:

Q: Find Lim 5e*-2x x-0 A. 5e C. 5 D. 0 B.

A: Solution

Q: B) Without using L'Hopital's rule, find: lim 3-Vx2+9 x2

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.